Trait malachite_base::num::arithmetic::traits::FloorRoot

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pub trait FloorRoot<POW> {
    type Output;

    fn floor_root(self, pow: POW) -> Self::Output;
}

Expand description

Finds the floor of the $n$th root of a number.

Required Associated Types

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Required Methods

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fn floor_root(self, pow: POW) -> Self::Output

Implementations on Foreign Types

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impl FloorRoot<u64> for u8

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fn floor_root(self, exp: u64) -> u8

Returns the floor of the $n$th root of a u8.

$f(x, n) = \lfloor\sqrt[n]{x}\rfloor$.

Notes

The u8 implementation uses lookup tables.

impl FloorRoot<u64> for u16

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fn floor_root(self, exp: u64) -> u16

Returns the floor of the $n$th root of a u16.

$f(x, n) = \lfloor\sqrt[n]{x}\rfloor$.

Notes

The u16 implementation calls the implementation for u32s.

impl FloorRoot<u64> for u32

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fn floor_root(self, exp: u64) -> u32

Returns the floor of the $n$th root of a u32.

$f(x, n) = \lfloor\sqrt[n]{x}\rfloor$.

For cube roots, the u32 implementation uses a piecewise Chebyshev approximation. For other roots, it uses Newton’s method. In both implementations, the result of these approximations is adjusted afterwards to account for error.

type Output = u32

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impl FloorRoot<u64> for u64

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fn floor_root(self, exp: u64) -> u64

Returns the floor of the $n$th root of a u64.

$f(x, n) = \lfloor\sqrt[n]{x}\rfloor$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero.

Examples

See here.

Notes

For cube roots, the u64 implementation uses a piecewise Chebyshev approximation. For other roots, it uses Newton’s method. In both implementations, the result of these approximations is adjusted afterwards to account for error.